The problem of compatible representatives
SIAM Journal on Discrete Mathematics
An outlet breaching algorithm for the treatment of closed depressions in a raster DEM
Computers & Geosciences
Proceedings of the 8th ACM international symposium on Advances in geographic information systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Higher order Delaunay triangulations
Computational Geometry: Theory and Applications
Hardness of Set Cover with Intersection 1
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Generating realistic terrains with higher-order Delaunay triangulations
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
The Complexity of Minimum Convex Coloring
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Partitioning graphs into connected parts
Theoretical Computer Science
An efficient depression processing algorithm for hydrologic analysis
Computers & Geosciences
An efficient depression processing algorithm for hydrologic analysis
Computers & Geosciences
Algorithm for dealing with depressions in dynamic landscape evolution models
Computers & Geosciences
On Partitioning a Graph into Two Connected Subgraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
I/O-efficient batched union-find and its applications to terrain analysis
ACM Transactions on Algorithms (TALG)
Bridge detection in grid terrains and improved drainage enforcement
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Flow computations on imprecise terrains
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
On partitioning a graph into two connected subgraphs
Theoretical Computer Science
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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In this paper we consider imprecise terrains, that is, triangulated terrains with a vertical error interval in the vertices. In particular, we study the problem of removing as many local extrema (minima and maxima) as possible from the terrain; that is, finding an assignment of one height to each vertex, within its error interval, so that the resulting terrain has minimum number of local extrema. We show that removing only minima or only maxima can be done optimally in O(nlogn) time, for a terrain with n vertices. Interestingly, however, the problem of finding a height assignment that minimizes the total number of local extrema (minima as well as maxima) is NP-hard, and is even hard to approximate within a factor of O(loglogn) unless P=NP. Moreover, we show that even a simplified version of the problem where we can have only three different types of intervals for the vertices is already NP-hard, a result we obtain by proving hardness of a special case of 2-Disjoint Connected Subgraphs, a problem that has lately received considerable attention from the graph-algorithms community.